Pregunta
The area of a circle is 1.5386 square centimeters. What is the circle's radius? Use \( \pi \approx 3.14 \) and round your answer to the nearest hundredth. \( \square \) centimeters
Ask by Smith Simmons. in the United States
Feb 05,2025
Solución de tutoría real
Respuesta verificada por el tutor
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The radius of the circle is \( 0.70 \) centimeters.
Solución
To find the radius of a circle given its area, you can use the formula for the area of a circle:
\[
A = \pi r^2
\]
Where:
- \( A \) is the area,
- \( \pi \) is approximately 3.14,
- \( r \) is the radius.
**Step-by-Step Solution:**
1. **Start with the area formula:**
\[
1.5386 = 3.14 \times r^2
\]
2. **Solve for \( r^2 \):**
\[
r^2 = \frac{1.5386}{3.14} = 0.49
\]
3. **Take the square root of both sides to find \( r \):**
\[
r = \sqrt{0.49} = 0.7 \text{ cm}
\]
4. **Round to the nearest hundredth:**
\[
r = 0.70 \text{ cm}
\]
**Answer:** \( 0.70 \) centimeters
Revisado y aprobado por el equipo de tutoría de UpStudy
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Extra Insights
To find the radius of the circle, we use the formula for the area of a circle: \( A = \pi r^2 \). Given that the area \( A = 1.5386 \) square centimeters and using \( \pi \approx 3.14 \), we can set up the equation: \[ 1.5386 = 3.14 r^2 \] Now, divide both sides by \( 3.14 \): \[ r^2 = \frac{1.5386}{3.14} \approx 0.4904 \] Next, we take the square root of \( r^2 \) to find \( r \): \[ r \approx \sqrt{0.4904} \approx 0.70 \] Therefore, the radius of the circle is approximately \( 0.70 \) centimeters.
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